A native of Burnaby, British Columbia,[1] Wotherspoon was selected by the Portland Winter Hawks in the second round of the 2008 Western Hockey League (WHL) bantam draft.

[7] Selected by the Calgary Flames with their second-round pick (57th overall) during the 2011 National Hockey League (NHL) entry draft,[8] Flames Special Assistant to General Manager Craig Conroy described Wotherspoon as a player whose qualities often go unnoticed: "If you're a stay-at-home defenceman that can join the rush, make the good first pass, doesn't get beat one-on-one, very sound, it doesn’t stand out.

"[1] Upon turning professional, Wotherspoon was assigned to Calgary's American Hockey League (AHL) affiliate, the Abbotsford Heat, for the 2013–14 season.

[1] He had nine points in his first 48 games and a plus-minus of +13 when an injury to defenceman Dennis Wideman late in the season caused the Flames to recall Wotherspoon on an emergency basis.

[10] Wotherspoon appeared in 14 games with the Flames, recording four assists, before suffering a shoulder injury that required surgery and ended his season.

[21] After five seasons within the Flames organization, Wotherspoon left as a free agent to sign a one-year, two-way contract with the St. Louis Blues on July 1, 2018.

[28] After participating in training camp and preseason, he was released from the PTO contract and signed a one-year deal with the Devils' AHL affiliate, the Utica Comets, on October 13, 2021.

[27] Following a successful season with the Comets in which he scored three goals and 21 points in 53 games, Wotherspoon was signed to a two-year, two-way contract by the Devils to continue within their organization on July 13, 2022.

[33][34][35] Wotherspoon's younger brother, Parker, was a fourth round selection by the New York Islanders in the 2015 NHL entry draft[36] and currently plays for the Boston Bruins.